Physical World Units and Measurements - Result Question 16

16. Which two of the following five physical parameters have the same dimensions? [2008]

(A) Energy density

(B) Refractive index

(C) Dielectric constant

(D) Young’s modulus

(E) Magnetic field

(a) (B) and (D)

(b) (C) and (E)

(c) (A) and (D)

(d) (A) and (E)

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Answer:

Correct Answer: 16. (c)

Solution:

  1. (c) Energy density $=\frac{\text{ Energy }}{\text{ Volume }}$

$\Rightarrow \frac{[ML^{2} T^{-2}]}{[L^{3}]}=[ML^{-1} T^{-2}]$

Refractive index and dielectric constant have no dimensions.

Young’s Modulus $=\frac{F}{A} \times \frac{l}{\Delta l}$

$\Rightarrow \frac{[MLT^{-2}]}{[L^{2}[.} \cdot \frac{[L]}{[L]}=[ML^{-1} T^{-2}]$.

Magnetic field, $B=\frac{F}{i \ell}=\frac{[MLT^{-2}]}{[A][L]}$

$ =[MT^{-2} A^{-1}] $